Chapter 3 - Derivatives - 3.9 Derivatives of Logarithmic and Exponential Functions - 3.9 Exercises - Page 211: 59

$\frac{dy}{dx} = \frac{-1}{x\ln(4)(\log_{4}(x))^2}$

$y = \frac{1}{\log_{4}(x)}$ Quotient Rule: $\frac{dy}{dx} = \frac{(0)(\log_{4}(x))-(1)\left(\frac{1}{x\ln(4)}\right)}{(\log_{4}(x))^2} = \frac{-1}{x\ln(4)(\log_{4}(x))^2}$